An Open-Label Phase II Study of the Combination of GSK2118436 and GSK1120212 in Patients With Metastatic Melanoma Which is Refractory or Resistant to BRAF Inhibitor

Study Drug Administration: If you are found to be eligible to take part in this study, you will take both dabrafenib and trametinib together. You will take 1 capsule of trametinib by mouth once a day. You will take 2 capsules of dabrafenib by mouth 2 times every day (1 time in the morning and 1 time in the evening, about 12 hours apart - a total of 4 capsules a day). If you experience severe side effects, your doctor or the research team may lower the dose of the drug(s). You should take the study drugs with about 1 cup (8 ounces) of room-temperature water. You should not eat or drink anything besides water for at least 1 hour before and 2 hours after you take the study drugs. You will be given a study drug diary to record the times and doses that you take the study drugs. You should bring the diary to each study visit. Study Visits: On Day 1 of Cycle 1: * Your medical history will be recorded, including any symptoms you may be having. (if it was not recorded in the previous 7 days) * Your weight, vital signs, and performance status will be recorded. * You will have a physical exam (if one was not performed in the previous 7 days). * Blood (about 2 teaspoons) will be collected for routine tests (if this was not performed in the previous 7 days). * You will be asked about any drugs you may be taking, how you are feeling, and if you have had any side effects. * You will have a blood draw this visit for research purposes. At some point between Day 4-10 of Cycle 1, you will have the same kind of biopsy that you had at screening. Your doctor and/or the study team will discuss this with you. On Days 8 of Cycle 1: * Your weight, vital signs, and performance status will be recorded. * Blood (about 4 tablespoons) will be drawn for biomarker testing. * You will be asked about any drugs or herbal supplements that you may be taking. * You will be asked about any drugs you may be taking, how you are feeling, and if you have had any side effects. On Day 15 of Cycle 1: * You will have a physical exam. * Your weight, vital signs, and performance status will be recorded. * You will have an ECG. * Blood (about 2 teaspoons) will be collected for routine tests. * Blood (about 4 tablespoons) will be drawn for biomarker testing. * You will be asked about any drugs you may be taking, how you are feeling, and if you have had any side effects. * If the disease has spread to the brain and your doctor thinks it is needed, you will have an MRI of the brain. On Day 1 of Cycles 2 and beyond: * You will have a physical exam. * Your weight, vital signs, and performance status will be recorded. * Blood (about 2 teaspoons) will be collected for routine tests. * You will be asked about any drugs you may be taking, how you are feeling, and if you have had any side effects * Blood (about 4 tablespoons) will be drawn for biomarker testing on day 1 of Cycle 2 and 4. If your disease worsens, blood (about 4 tablespoons) will also be drawn at that time. Every 8 weeks (2 cycles) from the time of the start of the treatment, you will have an x-ray, a CT scan, an MRI scan, a skin exam, and/or a bone scan to check the status of the disease. Every 12 weeks, you will have an ECHO performed. If at any point during the study you have any symptoms or signs of a serious skin, eye, or heart side effect, you may be referred to a dermatologist or an ophthalmologist, or you may have an ECG and ECHO to check your heart's health. Length of Study: You may continue taking the study drugs for as long as the study doctor thinks it is in your best interest. You will no longer be able to take the study drugs if the disease gets worse, you start having other health problems, or intolerable side effects occur. Your participation on the study will be over once you have completed the end-of-study visit. End-of-Study Visit: You will have an end-of-study visit within 4 weeks after your last dose of study drugs. The following tests and procedures will be performed: * You will have a physical exam. * Your weight, vital signs, and performance status will be recorded. * You will have an ECG. * Blood (about 2 teaspoons) will be collected for routine tests. You will have an x-ray, computed tomography (CT) scan, magnetic resonance imaging (MRI) scan, and/or bone scan to check the status of the disease if you are taken off the study for any other reason than the disease getting worse. * Blood (about 4 tablespoons) will be drawn for biomarker testing. * You will have the same kind of mandatory biopsy that you did at screening. You may be allowed to continue receiving the study drugs until the time of this biopsy (up to 2 days) even if the disease is not showing a response to the study drugs. Your doctor and/or the study team will discuss this with you. Survival Follow-Up: After you stop taking study drug, you will be followed approximately every 3 months (either clinic visit or contact by phone or letter) for 5 years or until death. If you are called, the call will last about 5 minutes. This is an investigational study. This is an investigational study. Both trametinib and dabrafenib are FDA approved and commercially available for the treatment of certain types of melanoma. Their use together in this study is investigational. Up to 45 patients will take part in this study. All will be enrolled at MD Anderson.